Time Master: Attempted Upgrade

"I have a uniform. I have a silenced pistol. I arrive in or near the Englischer Garten park. What time of year is it, when I arrive?"
The man nods and replies, "Again, that sounds reasonable. We hadn't thought about the season factor. You should arrive in early spring."
"What if it's raining, when I arrive, or even snowing?"
The man shakes his head in denial, then nods and replies, "Again, that sounds reasonable. We hadn't thought about the weather factor. We have weather records for the area that go back into the time when you'll arrive. We can select a time period when there should be no rain and no snow."
"Rain or snow would actually be better for me, as there would be less chance of someone seeing what I'm going to do, but the man might well not walk in the rain or snow. Now, if your people can check, was the man sick, during the target time?"
The man grins and replies, "That we did check. No, he wasn't sick, at least not sick enough to skip his usual morning walks in the park."
"So far, so good. Now, can your people tell me how the man might have been dressed? Just a verification on his identity."
The man shakes his head in denial, then replies, "Again, another thing that we need to check. You do need to make positive identification before you shoot."
"Alright, if it's cold enough, I can wear gloves. That should help, if I have to abandon the pistol, as there will be no fingerprints. I can also wear a hat. The hat, pulled down, will hide my identity. Of course, I didn't exist during the time that we're talking about, but it would help if the police don't even have someone to look for."
The man again shakes his head in denial, then replies, "Again, another thing that we need to check."
"I realize that you probably think that I'm being a bit picky, but I have a lot of experience with this sort of thing and none of your people do."
The man replies, "The assassination has to go exactly as planned. We have to set things up so that there's minimal chance for failure. We will now do a complete review of what we have planned. I can see that we skipped some of the detail and we'll go back and check at lower levels of detail."
"I would strongly suggest that you keep me in the planning loop. I'm the only one who has any real time travel experience and it's my life at risk. I tend to see things that others might miss and I'm very careful when I'm planning a time trip."
The man asks, "Is that all?"
"Not by quite a bit. First, we need to talk about my pay. Then we need to talk about a key item that only exists with time travel."
The man cautiously asks, "What would you expect in pay?"
"How does a time traveler feel when he arrives at his destination? How long does it take him to return to effective normal? Are there side effects? What if the time traveler can't get back to his return point?"
The man muses, "Yes, you're the only one who knows the answers to those questions."
"The answers to those questions and several other questions that I'm not going to go into, since that's how I earn my living, are what you're paying me for. Also, there's the danger factor, since I'm risking my life by working as as an assassin. If you want me to do the job, my fee will be one million United States dollars."